ns thnotion has long been overlooked in economicsmodels, although hehas advocators within psychology. For example, Runciman (1966)

1053-5357/$ doi:10.1016/j.sincome) by comparing it to the consumption (income)ers; see e.g. Solnick and Hemenway (1998), Johansson-al. (2002), Alpizar et al. (2005), and Andersson (2008).presents a general consumption model that is anersion of Alessie and Lusardis (1997) consumptionlessie and Lusardi (1997), individuals merely care aboutcurrent and previous consumption. I add the assump-dividuals also compare own consumptionwith that seenvant others, andderive a closed formconsumption func-arbitrary individual. Since an individuals consumptionds on the consumption by his relevant others, I intro-dividuals total marginal propensity to consume (totalier theories like Halls permanent income hypothesis1978), and a pure habit formation behavior model, suchnd Lusardi (1997), imply larger marginal propensities toan found in this model.listic that individuals only have their own previousn levels as reference? Probably not. From a psycholog-

ctive, individuals compare own consumption also withption levels of relevant others. Duesenberry (1949, p.that Any particular consumer will be inuenced byn of people with whom he has social contacts. . .;

31 773 2679.ress: fredrik.andersson@economics.gu.se.

argues that individuals have both a space and time dimension ofcomparison. Frank (1985, p. 146) presents an explanation to whyeconomists are not keen on adopting the space dimension: Tomany economists, the notion of consumers being strongly inu-enced by demonstration effects must have seemed troublinglyinconsistent with the reasoned pursuit of self-interest, if not com-pletely irrational. It seems reasonable to extend Alessie andLusardis (1997) model by including Duesenberrys demonstrationeffect. For example Frank (1985, p. 150) supports this by arguing:. . . concerns about relative standing are perfectly compatible withthe economists view that people pursue their own interest in arational way. I believe this extended consumption model addsmore knowledge about individuals actual consumption decision.1

This paper presents a closed form conon his own current and previous consmodel, I argue that we can introducein addition to the traditional denitionwhich I show is smaller than the tradi

tion he coitility

tion function for an individual when his utility depends bothion and on the consumption by his relevant others. Given thisernative denition of marginal propensity to consume (MPC)alternative denition can be called the individuals total MPC,l MPC.

2009 Elsevier Inc. All rights reserved.

is concept the demonstration effect. Duesenberrys

416 F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420

2. The individuals utility

2.1. The individuals utility function arguments

In order to emphasize how important individuals social inter-actions with each other are, Aristotle referred to human beings associal animals. By lookingatpsychological and sociologicalmotives,e.g. Duesenberry (1949), Runciman (1966), Frank (1985), and Elsterand Loewenstein (1992) argue that individuals have both a spaceand a time down currention of botprevious comentioneduals utilitythat peoplelevel, sinceLusardis (1consumptiosumption aindividual,

c = c c

where [0consumptiomore the inhow muchtion, and behavior. This previoudown to th = 0, and wused by, e.g

his pitiveindivimension of comparison. I.e., individuals compare theirt consumption with a reference level that is a func-h the consumption by relevant others and their ownnsumption. Compared to the two consumption modelsin Section 1 this adds more realism to what individ-depends on. Put differently, Scitovsky (1992) argueswish to keep their status in relation to their referencelosing status may be painful. Here I extend Alessie and997) model by assuming that people also care about thenamong relevantothers. Then, the psychological con-mount that utility depends on at time , for an arbitraryis:

1 c, (1)

,1] controls how much the individual cares about then among his relevant others,2c .3 The higher the , thedividual cares. The other parameter, [0,1], controlsthe individual cares about his own previous consump-> 0 implies that the individual has a habit-formationhe higher the , the more the individual cares abouts consumption. The formulation in Eq. (1) will then boile one used by Alessie and Lusardi (1997) for > 0 andhen = = 0 it will reect the conventional model as

. Hall (1978).

ividuals utility maximization problem

ption, the individuals utility, u(c), is concave, contin-wice differentiable over the interior of the individualsoreover I restrict the individuals consumption amount,s be non-negative.for the individual to optimize his consumption prole,predict at time his stock of human wealth, which isdiscounted value of his expected future labor incomeent value of his non-human wealth (a). I assume that theasanite life, givesnobequests atperiodT, dieswithoutnd lives in a world with a perfect capital market (i.e.,canborrowand lendat the sameconstant4 interest rate)he is not liquidity constrained. Furthermore, I assumeividual has perfect foresight about his own future laborthe future consumption among his relevant others; i.e.,tion is complete and there is no uncertainty.individuals intertemporal maximization problem canas

=T

=tu(c(c, c1, c)), (2)

thers refers to, e.g. neighbors, co-workers, and friends.ilar to thepsychological consumption thatAlonso-Carrera et al. (2004)hat analyzes the circumstancesunderwhich consumptionby relevantrce of inefciency. They also included a third reference argument,

revious consumption, ct1, of relevant others.st rate is independent of the capital stock in the economy.

whereunpaidfrom this not odies, htherefo

a +T

=

Whenral budconsumpresen

Furothersexogen

Thetime,wrules odoes n

Thesolvedporalproble

max{c

+

wheretion fo

L()ct

=

Since tfor t +L()ct+1

Then sby com

(u(ct(

= 11

Up to tan addof the=t

aT+1 0, (4)

nd c1 are given. Since the individual cannot havets at period T, aT+1 cannot be less than zero. Moreover,dividual intertemporal utility maximization problem, ital for the individual to have unused resources when heaT+1 = 0 will always hold. Constraints (3) and (4) can

e combined into:

1+ r)

y T

=t

(1

1 + r)

c = 0. (5)

interest rate, r, is constant over time, the intertempo-onstraint implies that the present discounted value ofn is equal to the individuals initial wealth (a) plus hiscounted labor income (y).ore, I assume that the consumption among relevant

ot affected by the individuals consumption; i.e., c isy given.viduals discount factor, = 1/(1 + ), is constant over > 0, and is the individuals pure timepreference. Thisy possibility of discontinuity of U (i.e., assures that Uverge to innity).ividuals intertemporal maximization problem is thenaximizing his lifetimeutility (2) subject to his intertem-et constraint (5). The Lagrangian function for this

(c, c+1, . . . ;) =T

=tu(c(c, c1, c))

+T

=t

(1

1 + r)

y T

=t

(1

1 + r)

c

), (6)

the constant Lagrange multiplier. The rst order condi-interior solution at an arbitrary period t is:

u(ct )ct

ctct

+ t+1u(ct+1)ct+1

ct+1ct

(

11 + r

)t= 0. (7)

xpression holds for all t, it is obvious that it also holds

+1 u(ct+1)

ct+1

ct+1ct+1

+ t+2u(ct+2)ct+2

ct+2ct+1

(

11 + r

)t+1(8)

g for the individualsmarginal rate of substitution (MRS)ng (7) and (8), we have (after some manipulation):

ct+1)(ct+1/ct+1)+(u(ct+2)/ct+2)(ct+2/ct+1)

)/ct )(ct /ct) + (u(ct+1)/ct+1)(ct+1/ct)

(9)

oint, the individuals MRS is valid for both a ratio andcomparison function. Let us continue the derivationiduals MRS with the additive comparison function as

F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420 417

in (1). Thus, Eq. (1) has the following properties for the additivecomparison function:

ctct

=ct+1ct+1

= 1, (10)

ct+1ct

=ct+2ct+1

= . (11)

Assuming that the individuals pure value of time preference isequal to the interest rate ( = r), the individuals MRS (9) may berewritten with the additional properties in (10) and (11) as

(u(ct+1)/(u(ct )/

Eq. (12) is s

u(ct )ct

=u

where ismarginal uover time ifcave utilitypsychologicconsumptio

Lemma 1.tion {ct }Tt=0

Hence,period t + 1increase insumption cderive the i

ct+1 = where ctsumption cconsumptiohis relevantAlessie and = 0 and H

3. The indi

The Eulehere possibtions in the

ct = (1 + g1

I use the asstion changereceive a simA consumpequation. W

5 My only inproblem.

6 In order toviduals consuuse the inform

7 This corredepends mereindividuals ut

possible to derive his closed form consumption function. By plac-ing (15) in (5), it is possible to write the individuals rst periodconsumption as

c0 =

(1 + g)+

at+ T

t=0

(1

1 + r)t

ytT2jt=2

Tj=0

jct

,(16)

where

= (1 + )(1 + r )r(1 + r)T , (17)+ g

r((1

) togtiseint.rdermpts precon

ulatio

1+ r)

Lemmn, wual:9

(1 +1 + r

(1(1 Eq.t timptio

g-uptureptio

esena haptio

ion fu

an eadinarys to Al

know

r)T )cnumbin thct+1) (u(ct+2)/ct+2)ct ) (u(ct+1)/ct+1)

= 1. (12)

atised if and only if:

(ct+1)ct+1

=u(ct+2)ct+2

= , t, (13)

a constant (see Appendix A for the proof), i.e., thetility of psychological consumption must be constantthe MRS between any two periods equals 1. Any con-function implies that when the marginal utility of

al consumption is constant, the level of psychologicaln is also constant c = constant. (see Lemma 1).Eq. (13) implies that the path of psychological consump-

is constant over time.

if the consumption by relevant others increases in, the individuals consumption in period t + 1 must alsoorder to keep the marginal utility of psychological con-onstant. By utilizing this knowledge, it is possible tondividuals consumption change:

ct + ct+1, (14)

+1 = ct+1 ct . This shows that the individuals con-hange in period t + 1 depends on his own previousn change and the current consumption changes amongothers.5 This is a general Euler equation that boils downLusardis (1997) consumption model when > 0 andalls PIH (1978) when = = 0.

viduals closed form consumption function

r equation is a recursive consumption function,which isle to rewrite as a function of the individuals consump-rst period as follows:6

) gt c0 +

T2j

t=2

Tj=0

jct

, t 2. (15)

umption that c1 = (1 + g)c0 (the individuals consump-dwith rate g between period t = 0 and t = 1) in order tople expression for the consumption in therst period.7

tion path derived from Eq. (15) will satisfy the Eulerhen I consider the individuals budget constraint it is

terest here is the interior solution to the intertemporal maximization

derive this equation I use the Euler equation. I rst dene the indi-mption in period t = 1. Then I lead the Euler equation one period andation from the consumption in period t = 1, and so forth.sponds to the case when the individuals utility in the rst periodly on past consumption. It is not until the second period that theility depends on the consumption by his relevant others.

to discuss one of the aims in this paper, I need to deriveion function for the individual that depends on the indi-vious consumption. Hence, I rewrite the intertemporalstraint (5) by substituting in c from (1), and after somen I solve for the present discounted value of c :8

c = c1 T

=t

(1

1 + r)

c

+[1

1 + r](

a +T

=t

(1

1 + r)

y

). (20)

a 1, I can derive from (20) a recursive consumptionhich satises the individuals budget constraint, for the

r)T 1)T+1 1

c1 i

+ (1 + r)T 1

(1 + r)T+1 1c

ii

r(1 + r)T+ r)T+1 1

T=t+1

(1

1 + r)

c

iii

1 + r)

r(1 + r)T(1 + r)T+1 1

[a +

T=t

(1

1 + r)

y

] iv

. (21)

(21) it follows that the individuals consumptione depends on four features: (i) a habit level ofnthe individuals own previous consumption, (ii) aeffect current consumption by relevant others, (iii) apotential disutility) of falling behind effect the futuren by relevant others, and (iv) the wealth effect, which ist in the PIH, although it is reduced when the individ-bit-formation behavior ( > 0).10 The general recursiven function in Eq. (21) boils down to two other con-nctions found in the literature: Halls (1978) PIH when

sily verify that if = 0, the intertemporal budget constraint collapsestextbook intertemporal budget constraint, and hence, if = 0, it

essie and Lusardis (1997) intertemporal budget constraint.

that Lemma 1 impliesT

=t(1/(1 + r))c = ((1 + r)T+1

.er of lagged variables depends on how many lagged variables aree c measure.

418 F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420

= = 0, which shows that an individuals consumption at time is equal to the annuity value of his lifetime resources and is constantover time, and the one in Alessie and Lusardi (1997), when > 0and = 0. The individuals consumption at time then dependspartly on his previous consumption and partly on his permanentincome.

3.1. The imp

It is posindividualshis relevantis the annuiand h umanand whereis the annusumption. T

path of the relevant others as painfuli.e., it reduces the individ-uals utility. This is captured by the last term in (25), where we cansee how the individuals consumption is negatively affected by hisrelevant others future consumption. Hence, the higher the futurepermanent consumption among his relevant others, the more theindividuals consumption at time is reduced.

sible to rewrite Eq. (21) by using concepts such as thepermanent income and the permanent consumption byothers,11 where the individuals permanent income (yp)ty valueof the sumof the currentnon-humanwealth (a)wealth (present discounted value of future income),

the permanent consumption by relevant others (cp+1)ity value of the present discounted value of future con-hus, the individuals consumption in period is:

+ c cp+1 +(1

1 + r)

yp, (22)

= ((1 + r)T 1)/((1 + r)T+1 1), yp = r(1 + r)T/1)(a +

T=t(1/(1 + r))

y), and cp+1 = r(1 + r)

T/

1)T

=t+1(1/(1 + r)) c .

ee from (22) that a change in permanent incomehas theon the individuals consumption as if the psychologi-

ption measure would merely include a habit formatione., the individuals utility depends on c = c c1.dividuals consumption changes with his permanent

+ r . (23)

3)we can see that if the individual increases his concernevious consumption, i.e., his habits, then a change in hisincome changes his consumption to a lesser extent.

11 + r < 0. (24)

individual has a negative change in his permanentnger habits (higher) implies that the individuals con-ecreases by a smaller amount than with weaker habits.er reduction comes from the fact that it takes time for

al to alter his consumption habits.

pact of the consumption by relevant others

s the consumption at time depend on a change in theoncern about the consumption by relevant others, i.e.,

cp+1ii

. (25)

uals consumption is affected in two ways: (i) The rsts from the individuals wish to keep up with the con-vels of his relevant others at time ; this is captured byin (25). This implies that the individuals consumption

s upward by a fraction of the current consumption byers, i.e., the individuals consumption to some degreeonsumption levels of his relevant others. (ii) The sec-rises if the individual perceives the future consumption

lso be possible to rewrite the permanent consumption by relevantanent income if we assume a constant saving rate.

12 Thisimpliespresentr a temporary increase in the consumption by relevanturrent time, . This may be for example a bonus, i.e.,ount of money. This increase boosts the individuals

sumption, since he wishes to keep up with them:

0. (26)

may impact the individuals consumption growth, andprovide some insight into why consumption growsincome.

ach of the past three years, real consumer outlays haveaster than real aftertax income.ss Week 17/4 2006 (U.S.: Its Way Too Early to Count

ers Out)

vidual knows that the consumption by relevant otherstime but not at time + 1. He will therefore increaseption at time to not lose status.

manent increase in the consumption by relevant

1934) states that it is the best-off members in a societysh the consumption standard for the rest, and then peo-ish to emulate their consumption. Duesenberry (1949,s that Low-income groups are affected by consump-

h-income groups but not vice versa., i.e., individualsrd comparisons when they evaluate their consumptionr thoughts, i.e., are voiced by, e.g. Schor (1998, p. 4)whoindividuals make comparison with, or choose, a refer-, people whose income are three, four, or ve times his. She nds that individuals with lower nancial statuseference groups save signicantly less than individualsnancial status than their reference groups.rease in the consumption by relevant others is perma-lso cp+1 changes and not just ct , then the individualsn changes as

1

= = ( 1) < 0, since < 1. (27)

ndividuals consumption is negatively affected by a per-sumption increase among relevant others.12

l propensity to consume

of marginal propensity to consume

1936, p. 36) argues that The fundamental psycholog-is that men are disposed, as a rule and on the average,their consumption as their income increases, but notas the increases in their income. Hence, the Keynesiann function hypothesizes that if an individuals currents/falls by oneunit, thenhis consumption should rise/fallllywith theMPC,which is less than1. This is theabsolute

is a result of the individuals intertemporal budget constraint, whichis present discounted value of consumption cannot be larger than thented value of his human and non-human wealth.

F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420 419

income hypothesis. Another venue is Friedmans (1957) permanentincome hypothesis, where MPC is determined by the relative vari-ations in permanent and transitory incomes. When the variationin permanent income is much greater than the variation in transi-tory income, consumption rises almost one-for-one with currentincome. Intuitively, an individuals consumption increases whenhis permanent income increases. Hall (1978) derives his versionof the permintertempoa proportioincome, anindividualsone. Duesethat once cfor an indivincome hypotain consumabandonedconsumptiosive consumimplicationand previoumodel of PIthe MPC islabor incom

We are nties to consLusardi (199

4.2. The ind

After deit is possibltional den

MPC dehis perm

This deallow the insumption apossible to

4.2.1. An incThe indi

Eq. (22):

c = c1

Differentiatsure of an iSection 3.1

mpc = cyp

Hence, if thincome, hisunits.We camuch he caindividualsmpc mpc

The otheHalls (1978

13 One unitincreases by o

MPC is:

mpcPIH = cyp

= 1. (30)

This implies that if the individuals permanent income is one unithigher, then

the ceve

s to eion oe thet (cion ot incforetakehers

totangeshe saers in

The cassut effenge it to ais he

al =

0 and 0 < < 1, it isformulate the following proposition:

1. When an individuals utility depends on both his ownprevious consumption in addition to the current consump-elevant others, his MPC is lower than if he had merely hadation behavior, as in Alessie and Lusardi (1997), while theighest in Halls (1978) PIH model.

the individual has both a habit-formation behavior ande degree about the consumption among his relevanthis consumption is less sensitive to an increase in hisincome and to the permanent consumption levels ofothers compared to if he merely has a habit-formationdobviously if onlyhis absolute consumptiondrives util-oothness depends on the fact that the individual doesfall behind the consumption among his relevant otherse, and therefore he adjusts his consumption level less.model may be better at explaining the excess smooth-omenon14 found in the consumption data compared tories, which opens up for further research.

eaton (1992).

420 F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420

5. Concluding remarks

By looking at psychological and sociological arguments of whatindividuals utility depends on, I extend Alessie and Lusardis(1997) consumptionmodel, inwhich individualsmerelyhavehabit-formation behaviors, by adding the notion that individuals also careabout the consumption among their relevant others. I also derivea general closed form consumption function that boils down tothe closed form consumption functions of Halls (1978) PIH, or ahabit-formation behavior such as in Alessie and Lusardis (1997)consumptio

The extconsumptioconsumptiosumption inwhen the cthe futureFurthermordoes not afthat the toAlessie andthat the indlevel of hismay be betup for furth

urrent consumption increases and (ii) decreases whenpermanent consumption by relevant others increases.e, a change in the consumption among relevant othersfect the individuals traditional MPC. However, I showtal MPC is lower compared to both Halls (1978) andLusardis (1997) MPC. This is a consequence of the factividual does not wish to fall behind the consumptionrelevant others in the future. Furthermore, this modelter at explaining the excess smoothness which openser research.be possible to test whether an individuals consump-s on both his own previous consumption and that seenelevant others, andwhether new information regardingals own future income and that among relevant otherse assumption of perfect foresight) affects consumption.ense analogous with papers in the happiness literature,irical evidence suggests that happiness of individualsy the income level of relevant others; see, e.g. Ferrer-i005).

gements

iate the thoughtful comments of Katarina Nordblom,son-Stenman, Hkan Locking, Wlodek Bursztyn, Johnrkus Knell, Debbie Axlid for editorial advices, and tworeferees for valuable comments on an earlier version of

that an individuals MRS under certain assumptions ise same as Eq. (12)):

ct+1) (u(ct+2)/ct+2)ct ) (u(ct+1)/ct+1)

= 1. (32)

2. The only admissible time series of psychological con- }T=t , that satises Eq. (32) when T is:(ct+1)

Grazividuals marginal utility of psychological consumptionover time. When an individuals utility function is con-is psychological consumption, ct+n, decreases over time,ies that his absolute consumption also decreases overs not a utility maximization, i.e., (2) is not maximized.osition 2 is true, and we can formulate Lemma 1.

., 2008. Is concern for relative consumption a function of relativeion? Journal of Socio-Economics 37 (1), 353364.ohansson-Stenman, O., 2008. When the Joneses consumption hurts:blic good provision and nonlinear income taxation. Journal of Public

34.nell, A., 2005. Income and well-being: an empirical analysis of then income effect. Journal of Public Economics 89 (56), 9971019.85. Choosing theRight Pond:HumanBehavior and theQuest for Status.iversity Press, Oxford.1957. A Theory of the Consumption Function. Princeton Universityceton.. Stochastic implication of the life-cycle-permanent income hypoth-y and evidence. The Journal of Political Economy 86 (6), 971987.nman, O., Carlsson, F., Daruvala, D., 2002. Measuring future grandpar-rences for equality and relative standing. The Economic Journal 112383.936. TheGeneral Theory of Employment, Interest andMoney.Macmil-n.G., 1966. Relative Deprivation and Social Justice. University of Califor-Berkeley.8. The Overspent American. Upscaling, Downshifting, and the New. Basic Books, New York.992. The Joyless Economy: The Psychology of Human Satisfaction.iversity Press, New York, Oxford.emenway, D., 1998. Is more always better? A survey on positionalJournal of Economic Behavior & Organization 37 (3), 373383.4. The Theory of the Leisure Class. Morden Library, New York.002. Habits:Multiplicative or Subtractive? Department of Economics,ersity, Mimeo.

The individual's closed form consumption functionThe impact of the individual's permanent incomeThe impact of the consumption by relevant othersA temporary increase in the consumption by relevant othersA permanent increase in the consumption by relevant others